Soft Computing

, Volume 21, Issue 8, pp 1923–1936

A novel soft rough fuzzy set: Z-soft rough fuzzy ideals of hemirings and corresponding decision making


DOI: 10.1007/s00500-016-2119-9

Cite this article as:
Zhan, J. & Zhu, K. Soft Comput (2017) 21: 1923. doi:10.1007/s00500-016-2119-9


This paper introduces the notion of Z-soft rough fuzzy sets of hemirings, which is an extended notion of soft rough sets and rough fuzzy sets. It is pointed out that this novel concept removes the limiting condition that full soft sets require in Feng-soft rough fuzzy sets and Meng-soft rough fuzzy sets. We study roughness in hemirings with respect to a ZS-approximation space. Some new soft rough fuzzy operations over hemirings are explored. In particular, Z-lower and Z-upper soft rough fuzzy ideals (k-ideals, h-ideals, strong h-ideals) are investigated. Finally, we put forth an approach for decision making problem based on Z-soft rough fuzzy sets and give an example. Corresponding decision making methods based on Z-soft rough fuzzy sets are analysed.


Soft rough fuzzy set Z-soft rough fuzzy set Z-soft rough fuzzy ideal Decision making 

Funding information

Funder NameGrant NumberFunding Note
National Natural Science Foundation of China
  • 11561023

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of MathematicsHubei University for NationalitiesEnshiChina

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